解题方法
1 . 如图.在正方形ABCD中,P,Q分别是AB,BC的中点,将
分别沿PD,PQ,DQ折起,使A,B,C三点重合于点M.
(2)证明:点M在平面PDQ的投影为
的垂心.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92dd2d73a5981c3315ba04cbaad6b35e.png)
(2)证明:点M在平面PDQ的投影为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a138fefcb02cc063b48967c0fc9d28f8.png)
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解题方法
2 . 如图,已知四棱柱
的底面
为矩形,E、F分别为线段
,
的中点.
平面
;
(2)若
,
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86aa0650b2b5cb33357dd45b241fd584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a570f7107fa7f02db45e9e16b1e33900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065bbb430087c19cb216e49bec97af3d.png)
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名校
3 . 如图,在四棱锥
中,
,
平面
分别为
的中点,
.
平面
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f089b54ee14e369cf48b528477a64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bf40f6235d0231481c2598e2ba977b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb46aaae98bce8e66848e09c2c1cdbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9801cabc43c024b9c5fac34b7db5d69b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5617a404c5a3356753136e5a6b6d51e5.png)
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4 . 如图,已知正四面体
的棱长为3.
的高;
(2)若球O的球面与正四面体
的棱有公共点.且球心O到正四面体
的四个面的距离相等,求球O的半径R的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
(2)若球O的球面与正四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
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解题方法
5 . 如图,在正三棱柱
中,
分别是
的中点.
为矩形
内动点,使得
面
,求线段
的最小值;
(2)求证:
面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0f13ea92fd3d07ff1d80d2525ed904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63646644bdc10fe8a669a61c592c8b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6dfed58659a9cab4d1836c3d2effdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9383df25a7d6d69d470086f54d525e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877bda7e850ca4a33e517fcf4a082b42.png)
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2卷引用:湖北省新高考联考协作体2023-2024学年高一下学期5月联考数学试题
名校
解题方法
6 . 如图,点
是棱长为2的正方体
的表面上一个动点,
是线段
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
A.存在点![]() ![]() |
B.若点![]() ![]() ![]() ![]() |
C.若点![]() ![]() ![]() ![]() |
D.当点![]() ![]() ![]() ![]() |
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昨日更新
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397次组卷
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3卷引用:浙江省重点中学四校2023-2024学年高一下学期5月联考数学试题
名校
解题方法
7 . 如图,已知四棱锥
的底面是正方形,点E是棱PA的中点,
平面ABCD.
平面BDE;
(2)求证:平面
平面BDE;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2597b5554284e275367c25529c6750f.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
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8 . 已知棱长为1的正方体
中.
;
(2)求直线
与平面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a28c816a483692b63e228cee6e8ac57.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
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9 . 如图,已知正方体
的棱长为1,O为底面ABCD的中心,
交平面
于点E,点F为棱CD的中点,则下列错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc6e94d7b0ad5b787681b709f1e9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d337cc486944076b459a4a9ad4bf0756.png)
A.三棱锥![]() ![]() |
B.异面直线BD与![]() ![]() |
C.点![]() ![]() ![]() |
D.过点![]() ![]() |
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解题方法
10 . 如图,在四棱锥
中,
平面PBC,底面ABCD为菱形,且
,E,F分别为BC,CD的中点.
;
(2)已知Q为棱BP上一点,且
,求证:
‖平面QAF.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95475bfc06e884754eb4a455c3f434e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d603566c74b1d5de510a2e8f7859010.png)
(2)已知Q为棱BP上一点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5518a06b5da9350e545b78d4c5f323f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
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